Diameter of universe

Can anyone explain how estimates of the diameter of universe are as high as something like 50 billion light-years while the age is about 12-13 billion light years (13 x 2 would seem to give diameter of 26)? Is this a function of the fact that the universe (especially during inflationary period) is expanding more rapidly than the speed of light in vacuum? How is this figure measured, or is it calculated?

This is a very common question. It has been answered well in several documents available over the internet, or from a good library.

Perhaps a good place would be Lineweaver's Scientific American article (sorry that I don't have the title or issue to hand); there's also a more technical paper by Lineweaver and Davis, on the same topic.

More generally, you might find Ned Wright's Cosmology Tutorial helpful in getting a grasp of the basics.

In the General Astronomy section, there is a sticky called A&C reference library. It's has a fantastic wealth of links; at the top of the last page (page 6!) is a post by marcus, with links to papers (etc) that address your questions, Hacky.

Hi Hacky! The short answer is the universe is temporally [time] bounded, but not spatially boundeed. This assumes there is 'nothing' outside the observable universe we can compare it to. But, this is not a bad assumption. If there is an 'outside' to our observable universe, we are unable to measure its properties, hence, we have no valid way to compare the properties of our universe to any others.

If you send a photon, after 12 billion years, the photon will be 12 billion light-years away from you in a static space. However, if the space between you and the photon is expanding, after 12 billion years the photon will be farther away from you than 12 billion light-years.

As I understand it, to begin with Stephen Hawking's example, the universe at the moment of the Big Bang was like a deflated balloon. The balloon has dots all over it which represent the galaxies in the universe. As the balloon is inflated (the Big Bang), all the dots (galaxies) expand away from each other. So if two dots had a third dot at their midpoint, and one dot expanded 1 inch from the midpoint, the other dot would now be 2 inches away since it also expanded from the midpoint by 1 inch. So since the universe expands at every point there's a mulitplier effect.
So what I heard is that since the universe has been expanding for 13.7 billion years, the total diameter of the universe, as a result of the additive expansions, is about 43 billion light years across.
But I may be wrong or just plain confusing :P

... the universe has been expanding for 13.7 billion years, the total diameter of the universe, as a result of the additive expansions, is about 43 billion light years across.

the estimate I think you are quoting is 46-47 billion lightyears and it is a RADIUS figure, not a diameter. That length is technically known as the particle horizon and it is the distance from us today, at the present moment, of the most distant particles that we can in principle be seeing today.

So that figure of 46-some billion LY is the radius of what is known as the (currently) observable universe.

It is confusing to speak of 46+ billion LY as "the radius of the universe" because it misleads people into thinking that it is the radius of the whole universe. It is not. The actual universe is known to be larger, and may indeed be infinite
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46+ billion LY is the current distance from us of farthest particles which today we could be pointing a dish or wave-detector or neutrino-eyeball at and at this moment be getting signals from. I speak figuratively about the technology.
Present technology has a way to go. At the present we dont have sensitive enough eyeballs and all we can see are particles which are 45 billion LY away. These are what sent us the light which eventually (after 13-some billion years) is being received by us as the cosmic microwave background. So we actually see 45, with present technology, and we could see 46. if we had instruments that could see stuff in the throes of the biggiebang.

In effect, 46+ billion LY is just the current size of a big ball with us as center which we call the (currently) observable universe.

the actual sure enough universe is bigger than that ball, and does not appear to have a center or a boundary, our notions of it are preliminary and somewhat vague.
If it is not infinite, which it could well be, then according to 2007 'best fit' to the available data it could have a circumference of
820 billion LY. This is a wildass guess which a professional, Ned Wright, just barely hinted at in a Jan 2007 scholarly paper if you read between the lines. At one point he gives a 'best fit' estimate of the overall curvature if the thing turns out to be finite and he does not translate that into a circumference, but 810-820 is what you get if you do translate.

Wow, you blew my mind. First I thought 13.7 billion light years was big, then 43, then 46, then 92, now about 820. It's ridiculous since I can't even comprehend 1 light year. And then there's my poor conception of eternity and infinity :) Does it really matter when I'll probably never even leave this planet :) However, it seems if there was a big bang, there has to be a point when everything was touching. If it expands as people commonly believe, that means it increases size from a previous smaller state. So that seems like it would need an edge or boundary so it could have an exterior space to expand into. So it could have a size or a limit. But if the big bang was "everything" coming into existence, it should include all space(s). So in a sense, there is no expansion and no diameter. Heaven in a mustard seed. Maybe this is how you get infinity or an infinite universe. Perhaps Einstein was right when he postulated that the universe could curve in on itself and become finite like a sphere, but infinite like its surface. And still there's an infinite number of points between the endpoints of a 1 inch line. Space can be divided infinitely and may expand infinitely. Time is also infinitely divided and can also be equated with space according to the term space-time. Thanks for your great response, that's the first time I've heard about that, including having watched educational tv shows and movies. Way too confusing :)

...it seems if there was a big bang, there has to be a point when everything was touching...

not sure where you got this idea. professional mainstream scientists do not say this (except in popularization books and media, where they are talking about the observable universe, but this doesnt come across)

it is not a part of the standard LCDM model of the universe that at one time everything was concentrated in a small volume or at a point
a singularity does not mean a point, a singularity can have infinite extent
all "singularity" means is where a theory breaks down, it can be along a whole infinite surface

as far as we know, singularities do not exist in nature----however they do exist in the classic vintage 1915 General Relativity theory: there are circumstances where it breaks down and fails to compute.

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maybe I should do a rough back-of-envelope calculation, somebody who knows please correct if this is off by too many orders of magnitude!

I think that the present density of the universe is about 10-29 times the density of water and Ashtekar's computer simulations of the quantum gravity big bounce tend to show a bounce when the density reaches 1093 times the density of water.

so the density at bangtime has to be about 10122 what it is today, for quantum effects to turn a collapse around and initiate expansion. This means that the radius of a representative volume has to be smaller by a factor of about 1040 or 1041

Well now we can take our volume to be the observable ball of universe surrounding us with a radius of 46 billion lightyears and a lightyear is about 1016 meters. So that radius is about 46 x 1025 meters
and what we are saying is that according to some QG computer runs, which is very preliminary and tentative indication at best, the radius would have to be shrunk by a factor of 1040 and so would be on the order of 46 x 10-15 meters

I'd say that borders on downright incredible. Either it is incomprehensible or at some point when you compress enough it must be true that matter and space are the same thing---geometry itself is able to absorb energy and become a seething mess----spatial relationship and matter become an indistinguishable writhing tangle with a very high specific heat so it can absorb enormous amounts of energy. A theory of quantum geometry has to somehow account for a phase change at these very high densities and pressures---not just phase of matter but phase of geometry itself must undergo change. This is my two-cents hunch.

After all that estimated radius is 10-14 meters and that is a tenthousandth of an angstrom. In other words a tenthousandth of the size of an atom. Maybe it doesn't happen. We don't understand the bounce. Some big bounce models have it happen at lower density than the recent computer simulations by Ashtekar's group. Maybe Ashtekar's model is wrong and it doesn't ever get that high. That is Planck-scale density.

Or maybe i have made an arithmetic mistake. Anyway. It is too early to try to say what conditions were really like just prior to the beginning of expansion.

The OBSERVABLE universe could at one time have been concentrated in a small volume, sort of like you imagine. I confess that is pretty mindboggling itself. The observable universe is now a ball with us as center and a radius of some 46 billion LY!

Can anyone explain how estimates of the diameter of universe are as high as something like 50 billion light-years while the age is about 12-13 billion light years (13 x 2 would seem to give diameter of 26)? Is this a function of the fact that the universe (especially during inflationary period) is expanding more rapidly than the speed of light in vacuum? How is this figure measured, or is it calculated?

Thanks, Howard

I think that I can answer your question. It deals with something called inflation theory, which basically states that at the birth of our universe it quite literally inflated at an exponential rate (10^50 something I believe) for millions of years until it finally cooled down (in which case atoms could finally form and multiply. Other high elements were also created at this stage). After initial inflation was over, the universes expansion slowed until it was caught by something called dark energy which is now the cause of our universes accelerated expansion. So, the universe can have a diameter of about 93 billion LY but only an age of 13.7 LY because it expanded much faster than the speed of light during its birth.
hope this helped